Dzhaparidze and van Zanten (2004, 2004b) proved an explicit series expansion of the multi-parameter fractional Brownian sheet. We extend their results to a certain class of isotropic Gaussian random fields with homogeneous increments, In particular, this class contains the multi-parameter fractional Brownian motion. Let ξ(x) be a centred mean-square continuous Gaussian random field with homogen...

We introduce the concept of augmented watermarking in which in addition to the hidden watermark placed within the image an explicit watermark-dependent random sequence (noise) is added to it. The receiver first detects the watermark, computes the random sequence for which the watermark serves as the seed, and then subtracts out this random sequence. This system can be devised with several water...

A simple random walk on a graph is defined in which a particle moves from one vertex to any adjacent vertex, each with equal probability. The expected hitting time is the expected number of steps to get from one vertex to another before returning to the starting vertex. In this paper, using the electrical network approach, we provide explicit formulae for expected hitting times for simple rando...

Population dynamics models remain largely deterministic, although the presence of random fluctuations in nature is well recognized. This deterministic approach is based on the implicit assumption that systems can be separated into a deterministic part that captures the essential features of the system and a random part that can be neglected. But is it possible, in general, to understand populat...

Homology has long been accepted as an important computable tool for quantifying complex structures. In many applications, these structures arise as nodal domains of real-valued functions and are therefore amenable only to a numerical study based on suitable discretizations. Such an approach immediately raises the question of how accurate the resulting homology computations are. In this paper, w...

This paper investigates self-organizing binary majority consensus disturbed by 1 faulty nodes with random and persistent failure. We study consensus in ordered and random 2 networks with noise, message loss, and delays. Using computer simulations, we show that: 3 (a) explicit randomization by noise, message loss, and topology can increase robustness 4 towards faulty nodes, (b) commonly-used fau...

Dictionaries are collections of vectors used for representations of random vectors in Euclidean spaces. Recent research on optimal dictionaries is focused on constructing dictionaries that offer sparse representations, i.e., l0-optimal representations. Here we consider the problem of finding optimal dictionaries with which representations of samples of a random vector are optimal in an l2-sense...

New Vapnik–Chervonenkis type concentration inequalities are derived for the empirical distribution of an independent random sample. Focus is on maximal deviation over classes Borel sets within a low probability region. The constants explicit, enabling numerical comparisons.

Abstract Benford’s law states that for many random variables X > 0 its leading digit D = D(X) satisfies approximately the equation P(D = d) = log10(1 + 1/d) for d = 1, 2, . . . , 9. This phenomenon follows from another, maybe more intuitive fact, applied to Y := log10 X: For many real random variables Y , the remainder U := Y − ⌊Y ⌋ is approximately uniformly distributed on [0, 1). The present ...

This paper presents a set of benchmarks and metrics for performance reporting in explicit state parallel model checking algorithms. The benchmarks are selected for controllability, and the metrics are chosen to measure speedup and communication overhead. The benchmarks and metrics are used to compare two parallel model checking algorithms: partition and random walk. Implementations of the parti...